void MakeExplicitlyHermitian( UpperOrLower uplo, DistMatrix<F,MC,MR>& A )
{
const Grid& g = A.Grid();
DistMatrix<F,MC,MR> ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F,MC,MR> A11Adj(g);
DistMatrix<F,MR,MC> A11_MR_MC(g);
DistMatrix<F,MR,MC> A21_MR_MC(g);
DistMatrix<F,MR,MC> A12_MR_MC(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A11Adj.AlignWith( A11 );
A11_MR_MC.AlignWith( A11 );
A12_MR_MC.AlignWith( A21 );
A21_MR_MC.AlignWith( A12 );
//--------------------------------------------------------------------//
A11_MR_MC = A11;
A11Adj.ResizeTo( A11.Height(), A11.Width() );
Adjoint( A11_MR_MC.LocalMatrix(), A11Adj.LocalMatrix() );
if( uplo == LOWER )
{
MakeTrapezoidal( LEFT, UPPER, 1, A11Adj );
Axpy( (F)1, A11Adj, A11 );
A21_MR_MC = A21;
Adjoint( A21_MR_MC.LocalMatrix(), A12.LocalMatrix() );
}
else
{
MakeTrapezoidal( LEFT, LOWER, -1, A11Adj );
Axpy( (F)1, A11Adj, A11 );
A12_MR_MC = A12;
Adjoint( A12_MR_MC.LocalMatrix(), A21.LocalMatrix() );
}
//--------------------------------------------------------------------//
A21_MR_MC.FreeAlignments();
A12_MR_MC.FreeAlignments();
A11_MR_MC.FreeAlignments();
A11Adj.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
int main()
{
DoubleMatrix A(3,3);
DoubleInterval A00(2,3);
DoubleInterval A10(5,9);
DoubleInterval A11(3,4);
DoubleInterval A20(-2,5);
DoubleInterval A21(3,8);
A(0,0) = A00;
A(0,1) = 0;
A(0,2) = 0;
A(1,0) = A10;
A(1,1) = A11;
A(1,2) = 0;
A(2,0) = A20;
A(2,1) = A21;
A(2,2) = 5;
DoubleInterval X(0,0);
mtl::dense_vector<DoubleInterval> b(3,X);
b[0] = 5;
b[1] = 3;
b[2] = -6;
mtl::dense_vector<DoubleInterval> x(3,X);
x = mtl::mat::upper_trisolve(A,b);
std::cout << x << std::endl;
return 0;
}
std::string makeFormattedString(
const char* aFormat,
const A1& a1 = A1(),
const A2& a2 = A2(),
const A3& a3 = A3(),
const A4& a4 = A4(),
const A5& a5 = A5(),
const A6& a6 = A6(),
const A7& a7 = A7(),
const A8& a8 = A8(),
const A9& a9 = A9(),
const A10& a10 = A10(),
const A11& a11 = A11(),
const A12& a12 = A12(),
const A13& a13 = A13(),
const A14& a14 = A14(),
const A15& a15 = A15(),
const A16& a16 = A16(),
const A17& a17 = A17(),
const A18& a18 = A18(),
const A19& a19 = A19(),
const A20& a20 = A20()
)
{
return makeStringByPrintf(aFormat,
a1, a2, a3, a4, a5, a6, a7, a8, a9, a10,
a11, a12, a13, a14, a15, a16, a17, a18, a19, a20
);
}
void graphics::NgoiLang(QPainter& painter,int x,int y,int c,int r)
{
QPoint A(x-r/2,y+c);
QPoint B(x+r/2,y+c);
QPoint C(x+r/2,y+c/3);
QPoint D(x,y);
QPoint E(x-r/2,y+c/3);
QPolygon poly1;
poly1 << D << E << A << B << C;
painter.drawPolygon(poly1);
// ve cai cua
QPoint A1(x,y+c);
QPoint B1(x,y+2*c/3);
QPoint C1(x-r/4,y+2*c/3);
QPoint D1(x-r/4,y+c);
QPolygon poly2;
poly2 << A1 << B1 << C1 << D1;
painter.drawPolyline(poly2);
// ve cua so
QPoint A11(x-r/4,y+c/6);
QPoint B11(x-r/4,y);
QPoint C11(x-r/8,y);
QPoint D11(x-r/8,y+c/12);
QPolygon poly21;
poly21 << A11 << B11 << C11 << D11;
painter.drawPolygon(poly21);
painter.drawRect(x+r/4,y+c/2.5,c/10,r/10);
}
int main()
{
Rat a1(-1,2);
Rat a2(2,9);
Rat b2(3,2);
Rat c1(-1,9);
DoubleInterval A11(a2,b2);
DoubleInterval A12(a1,0);
DoubleInterval A21(-1,c1);
DoubleInterval A22(a2,b2);
DoubleMatrix A(2,2);
A(0,0) = A11;
A(0,1) = A12;
A(1,0) = A21;
A(1,1) = A22;
DoubleInterval B1(1,3);
DoubleInterval B2(3,4);
DoubleVector b(2, (DoubleInterval)0);
b[0] = B1;
b[1] = B2;
std::cout << A << std::endl;
std::cout << b << std::endl;
DoubleVector x(2, (DoubleInterval)0);
x = A * b;
std::cout << x << std::endl;
//Need to sort this out
DoubleInterval test(-1,2);
DoubleInterval testb(5,100);
DoubleInterval ans;
ans = testb/test;
std::cout << ans << std::endl;
DoubleInterval k00(0,2);
DoubleInterval k01(1,3);
DoubleInterval k10(3,5);
DoubleInterval k11(5,7);
std::cout << "INVERSE IS " << std::endl;
std::cout << boost::numeric::Doubleinterval_lib::multiplicative_inverse(k11) << std::endl;
std::cout << boost::numeric::norm(k11) << std::endl;
std::cout << k00 * k11 << std::endl;
std::cout << k01 * k10 << std::endl;
std::cout << (k00 * k11) - (k01 * k10) << std::endl;
return 0;
}
int main()
{
const int sz=7;
CArray A(sz);
A(0) = complex<float>(1,2);
A(1) = complex<float>(3,4);
Array<float,1> Ar = real(A);
BZTEST(int(Ar(0)) == 1 && int(Ar(1)) == 3);
Array<float,1> Ai = imag(A);
BZTEST(int(Ai(0)) == 2 && int(Ai(1)) == 4);
CArray Ac(sz);
Ac = conj(A);
BZTEST(Ac(0) == complex<float>(1,-2));
BZTEST(Ac(1) == complex<float>(3,-4));
Array<float,1> Ab(sz);
Ab = abs(A);
BZTEST(fabs(Ab(0) - 2.236068) < eps);
BZTEST(fabs(Ab(1) - 5.0) < eps);
Ab = arg(A);
BZTEST(fabs(Ab(0) - atan(2.0)) < eps);
BZTEST(fabs(Ab(1) - atan(4.0/3.0)) < eps);
Array<float,1> r(sz), theta(sz);
r(0) = 4.0f;
r(1) = 15.0f;
theta(0) = float(3.141592/3.0);
theta(1) = float(3.0*3.141592/2.0);
Ac = blitz::polar(r,theta);
BZTEST(fabs(real(Ac(0)) - 2) < eps);
BZTEST(fabs(imag(Ac(0)) - 3.4641012) < eps);
BZTEST(fabs(real(Ac(1)) - 0.0) < eps);
BZTEST(fabs(imag(Ac(1)) + 15.0) < eps);
Array<complex<long double>,1> A11(5),B11(5),C11(5);
A11=1,2,3,4,5;
B11=1,2,3,4,5;
C11=A11+B11;
BZTEST(fabs(real(C11(0)) - 2.) < eps);
C11=A11/B11;
BZTEST(fabs(real(C11(1)) - 1.) < eps);
C11=1.0l/A11;
BZTEST(fabs(real(C11(2)) - 1/3.) < eps);
C11=A11/1.0l;
BZTEST(fabs(real(C11(3)) - 4.) < eps);
C11=complex<long double>(0,1)/A11;
BZTEST(fabs(imag(C11(4)) - 1/5.) < eps);
C11=A11/complex<long double>(0,1);
BZTEST(fabs(imag(C11(0)) - -1.) < eps);
return 0;
}
inline void
LQ( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("LQ");
#endif
if( IsComplex<R>::val )
throw std::logic_error("Called real routine with complex datatype");
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g), ATopPan(g), ABottomPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
ATopPan.View1x2( A11, A12 );
ABottomPan.View1x2( A21, A22 );
//--------------------------------------------------------------------//
internal::PanelLQ( ATopPan );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, FORWARD, 0, ATopPan, ABottomPan );
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
SymmLLC
( T alpha, const DistMatrix<T>& A, const DistMatrix<T>& B,
T beta, DistMatrix<T>& C )
{
#ifndef RELEASE
PushCallStack("internal::SymmLLC");
if( A.Grid() != B.Grid() || B.Grid() != C.Grid() )
throw std::logic_error
("{A,B,C} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<T>
ATL(g), ATR(g), A00(g), A01(g), A02(g), AColPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g), ARowPan(g),
A20(g), A21(g), A22(g);
DistMatrix<T>
BT(g), B0(g),
BB(g), B1(g),
B2(g);
DistMatrix<T>
CT(g), C0(g), CAbove(g),
CB(g), C1(g), CBelow(g),
C2(g);
// Temporary distributions
DistMatrix<T,MC, STAR> AColPan_MC_STAR(g);
DistMatrix<T,STAR,MC > ARowPan_STAR_MC(g);
DistMatrix<T,MR, STAR> B1Trans_MR_STAR(g);
B1Trans_MR_STAR.AlignWith( C );
// Start the algorithm
Scale( beta, C );
LockedPartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDown
( B, BT,
BB, 0 );
PartitionDown
( C, CT,
CB, 0 );
while( CB.Height() > 0 )
{
LockedRepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDown
( BT, B0,
/**/ /**/
B1,
BB, B2 );
RepartitionDown
( CT, C0,
/**/ /**/
C1,
CB, C2 );
LockedView1x2( ARowPan, A10, A11 );
LockedView2x1
( AColPan, A11,
A21 );
View2x1
( CAbove, C0,
C1 );
View2x1
( CBelow, C1,
C2 );
AColPan_MC_STAR.AlignWith( CBelow );
ARowPan_STAR_MC.AlignWith( CAbove );
//--------------------------------------------------------------------//
AColPan_MC_STAR = AColPan;
ARowPan_STAR_MC = ARowPan;
MakeTrapezoidal( LEFT, LOWER, 0, AColPan_MC_STAR );
MakeTrapezoidal( RIGHT, LOWER, -1, ARowPan_STAR_MC );
B1Trans_MR_STAR.TransposeFrom( B1 );
LocalGemm
( NORMAL, TRANSPOSE,
alpha, AColPan_MC_STAR, B1Trans_MR_STAR, T(1), CBelow );
LocalGemm
( TRANSPOSE, TRANSPOSE,
alpha, ARowPan_STAR_MC, B1Trans_MR_STAR, T(1), CAbove );
//--------------------------------------------------------------------//
AColPan_MC_STAR.FreeAlignments();
ARowPan_STAR_MC.FreeAlignments();
SlideLockedPartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDown
( BT, B0,
B1,
/**/ /**/
BB, B2 );
SlidePartitionDown
( CT, C0,
C1,
/**/ /**/
CB, C2 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrsmUVar1
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrsmUVar1");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( U.Height() != U.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != U.Height() )
LogicError("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,VC, STAR> U01_VC_STAR(g);
DistMatrix<F,VR, STAR> U01_VR_STAR(g);
DistMatrix<F,STAR,MR > U01Adj_STAR_MR(g);
DistMatrix<F,STAR,STAR> X11_STAR_STAR(g);
DistMatrix<F,MR, MC > Z01_MR_MC(g);
DistMatrix<F,MC, STAR> Z01_MC_STAR(g);
DistMatrix<F,MR, STAR> Z01_MR_STAR(g);
DistMatrix<F> Y01(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A01_VC_STAR.AlignWith( A01 );
U01_MC_STAR.AlignWith( A00 );
U01_VR_STAR.AlignWith( A00 );
U01_VC_STAR.AlignWith( A00 );
U01Adj_STAR_MR.AlignWith( A00 );
Y01.AlignWith( A01 );
Z01_MR_MC.AlignWith( A01 );
Z01_MC_STAR.AlignWith( A00 );
Z01_MR_STAR.AlignWith( A00 );
//--------------------------------------------------------------------//
// Y01 := A00 U01
U01_MC_STAR = U01;
U01_VR_STAR = U01_MC_STAR;
U01Adj_STAR_MR.AdjointFrom( U01_VR_STAR );
Zeros( Z01_MC_STAR, A01.Height(), A01.Width() );
Zeros( Z01_MR_STAR, A01.Height(), A01.Width() );
LocalSymmetricAccumulateLU
( ADJOINT,
F(1), A00, U01_MC_STAR, U01Adj_STAR_MR, Z01_MC_STAR, Z01_MR_STAR );
Z01_MR_MC.SumScatterFrom( Z01_MR_STAR );
Y01 = Z01_MR_MC;
Y01.SumScatterUpdate( F(1), Z01_MC_STAR );
// A01 := inv(U00)' A01
//
// This is the bottleneck because A01 only has blocksize columns
Trsm( LEFT, UPPER, ADJOINT, diag, F(1), U00, A01 );
// A01 := A01 - 1/2 Y01
Axpy( F(-1)/F(2), Y01, A01 );
// A11 := A11 - (U01' A01 + A01' U01)
A01_VC_STAR = A01;
U01_VC_STAR = U01_MC_STAR;
Zeros( X11_STAR_STAR, A11.Height(), A11.Width() );
Her2k
( UPPER, ADJOINT,
F(-1), A01_VC_STAR.Matrix(), U01_VC_STAR.Matrix(),
F(0), X11_STAR_STAR.Matrix() );
A11.SumScatterUpdate( F(1), X11_STAR_STAR );
// A11 := inv(U11)' A11 inv(U11)
A11_STAR_STAR = A11;
U11_STAR_STAR = U11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// A01 := A01 - 1/2 Y01
Axpy( F(-1)/F(2), Y01, A01 );
// A01 := A01 inv(U11)
A01_VC_STAR = A01;
LocalTrsm
( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
}
inline void
Householder( DistMatrix<F>& A, DistMatrix<F,MD,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("qr::Householder");
if( A.Grid() != t.Grid() )
LogicError("{A,s} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
if( t.Viewing() )
{
if( !t.AlignedWithDiagonal( A ) )
LogicError("t was not aligned with A");
}
else
{
t.AlignWithDiagonal( A );
}
t.ResizeTo( Min(A.Height(),A.Width()), 1 );
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g), ALeftPan(g), ARightPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F,MD,STAR>
tT(g), t0(g),
tB(g), t1(g),
t2(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
View2x1
( ALeftPan, A11,
A21 );
View2x1
( ARightPan, A12,
A22 );
//--------------------------------------------------------------------//
PanelHouseholder( ALeftPan, t1 );
ApplyQ( LEFT, ADJOINT, ALeftPan, t1, ARightPan );
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
internal::HermitianTridiagU( DistMatrix<R,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::HermitianTridiagU");
if( A.Height() != A.Width() )
throw std::logic_error( "A must be square." );
#endif
const Grid& g = A.Grid();
if( g.InGrid() )
{
// Matrix views
DistMatrix<R,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<R,MC, MR > WPan(g);
DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<R,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g),
A11_MC_STAR(g);
DistMatrix<R,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g),
A11_MR_STAR(g);
DistMatrix<R,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g),
W11_MC_STAR(g);
DistMatrix<R,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g),
W11_MR_STAR(g);
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
if( A00.Height() > 0 )
{
WPan.AlignWith( A01 );
APan_MC_STAR.AlignWith( A00 );
WPan_MC_STAR.AlignWith( A00 );
APan_MR_STAR.AlignWith( A00 );
WPan_MR_STAR.AlignWith( A00 );
//------------------------------------------------------------//
WPan.ResizeTo( ATL.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
internal::HermitianPanelTridiagU
( ATL, WPan,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionUp
( APan_MC_STAR, A01_MC_STAR,
A11_MC_STAR, A11.Height() );
PartitionUp
( APan_MR_STAR, A01_MR_STAR,
A11_MR_STAR, A11.Height() );
PartitionUp
( WPan_MC_STAR, W01_MC_STAR,
W11_MC_STAR, A11.Height() );
PartitionUp
( WPan_MR_STAR, W01_MR_STAR,
W11_MR_STAR, A11.Height() );
internal::LocalTrr2k
( UPPER, TRANSPOSE, TRANSPOSE,
(R)-1, A01_MC_STAR, W01_MR_STAR,
W01_MC_STAR, A01_MR_STAR,
(R)1, A00 );
//------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
HermitianTridiag( UPPER, A11_STAR_STAR.LocalMatrix() );
A11 = A11_STAR_STAR;
}
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
}
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::HermitianTridiagU
( DistMatrix<Complex<R>,MC, MR >& A,
DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
PushCallStack("internal::HermitianTridiagU");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( t.Viewing() )
throw std::logic_error("t must not be a view");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
DistMatrix<C,MD,STAR> tDiag(g);
tDiag.AlignWithDiagonal( A, 1 );
tDiag.ResizeTo( A.Height()-1, 1 );
if( g.InGrid() )
{
// Matrix views
DistMatrix<C,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<C,MD,STAR> tT(g), t0(g),
tB(g), t1(g),
t2(g);
// Temporary distributions
DistMatrix<C,MC, MR > WPan(g);
DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
DistMatrix<C,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<C,MC, STAR> APan_MC_STAR(g), A01_MC_STAR(g),
A11_MC_STAR(g);
DistMatrix<C,MR, STAR> APan_MR_STAR(g), A01_MR_STAR(g),
A11_MR_STAR(g);
DistMatrix<C,MC, STAR> WPan_MC_STAR(g), W01_MC_STAR(g),
W11_MC_STAR(g);
DistMatrix<C,MR, STAR> WPan_MR_STAR(g), W01_MR_STAR(g),
W11_MR_STAR(g);
PartitionUpDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionUp
( tDiag, tT,
tB, 0 );
while( ABR.Height() < A.Height() )
{
RepartitionUpDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
RepartitionUp
( tT, t0,
t1,
/**/ /**/
tB, t2 );
if( A00.Height() > 0 )
{
WPan.AlignWith( A01 );
APan_MC_STAR.AlignWith( A00 );
WPan_MC_STAR.AlignWith( A00 );
APan_MR_STAR.AlignWith( A00 );
WPan_MR_STAR.AlignWith( A00 );
//------------------------------------------------------------//
WPan.ResizeTo( ATL.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ATL.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ATL.Height(), A11.Width() );
internal::HermitianPanelTridiagU
( ATL, WPan, t1,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionUp
( APan_MC_STAR, A01_MC_STAR,
A11_MC_STAR, A11.Height() );
PartitionUp
( APan_MR_STAR, A01_MR_STAR,
A11_MR_STAR, A11.Height() );
PartitionUp
( WPan_MC_STAR, W01_MC_STAR,
W11_MC_STAR, A11.Height() );
PartitionUp
( WPan_MR_STAR, W01_MR_STAR,
W11_MR_STAR, A11.Height() );
internal::LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
(C)-1, A01_MC_STAR, W01_MR_STAR,
W01_MC_STAR, A01_MR_STAR,
(C)1, A00 );
//------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
t1_STAR_STAR.ResizeTo( t1.Height(), 1 );
HermitianTridiag
( UPPER, A11_STAR_STAR.LocalMatrix(),
t1_STAR_STAR.LocalMatrix() );
A11 = A11_STAR_STAR;
t1 = t1_STAR_STAR;
}
SlidePartitionUp
( tT, t0,
/**/ /**/
t1,
tB, t2 );
SlidePartitionUpDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
}
}
// Redistribute from matrix-diagonal form to fully replicated
t = tDiag;
#ifndef RELEASE
PopCallStack();
#endif
}
int main()
{
std::cout << "============== Test 1 ==============" << std::endl << std::endl;
DoubleInterval A00(2,3);
DoubleInterval A01(0,1);
DoubleInterval A10(1,2);
DoubleInterval A11(2,3);
DoubleInterval B0(0,120);
DoubleInterval B1(60,240);
DoubleMatrix *A = new DoubleMatrix(2,2);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A: " << std::endl;
std::cout << *A << std::endl;
DoubleVector *b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b: " << std::endl;
std::cout << *b << std::endl << std::endl;
DoubleVector *x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
//Solution should be [[-120,90], [-60,240]]^T
delete A;
delete b;
delete x;
/*std::cout << "============== Test 2 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 2;
(*A)(0,1) = 1;
(*A)(0,2) = -1;
(*A)(1,0) = -3;
(*A)(1,1) = -1;
(*A)(1,2) = 2;
(*A)(2,0) = -2;
(*A)(2,1) = 1;
(*A)(2,2) = 2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -11;
(*b)[2] = -3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Solution should be [2, 3, -1]^T
std::cout << "============== Test 3 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
(*A)(0,0) = 1;
(*A)(0,1) = -2;
(*A)(1,0) = 2;
(*A)(1,1) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = 3;
(*b)[1] = 9;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Solution should be [5, 1]^T
std::cout << "============== Test 4 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 2;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(1,0) = 1;
(*A)(1,1) = 1;
(*A)(1,2) = 1;
(*A)(2,0) = 3;
(*A)(2,1) = 4;
(*A)(2,2) = 2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 1;
(*b)[1] = 3;
(*b)[2] = 4;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 5 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(1,0) = 1;
(*A)(1,1) = 1;
(*A)(1,2) = -1;
(*A)(2,0) = 3;
(*A)(2,1) = 11;
(*A)(2,2) = 5;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 9;
(*b)[1] = 1;
(*b)[2] = 35;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 6 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,2);
(*A)(0,0) = 1;
(*A)(0,1) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = 3;
(*A)(2,0) = 3;
(*A)(2,1) = -2;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be an exact solution as even though the system is overdetermined but
//as the Rank is 2 and the amount of unknowns is 2
std::cout << "============== Test 7 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
(*A)(0,0) = 1;
(*A)(0,1) = 1;
(*A)(0,2) = 1;
(*A)(0,3) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = 3;
(*A)(1,2) = -1;
(*A)(1,3) = -1;
(*A)(2,0) = 3;
(*A)(2,1) = 2;
(*A)(2,2) = 1;
(*A)(2,3) = 1;
(*A)(3,0) = 3;
(*A)(3,1) = 6;
(*A)(3,2) = -1;
(*A)(3,3) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 2;
(*b)[2] = 5;
(*b)[3] = 4;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be no solutions as the system is inconsistent
std::cout << "============== Test 8 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,3);
(*A)(0,0) = -1;
(*A)(0,1) = 2;
(*A)(0,2) = -1;
(*A)(1,0) = -2;
(*A)(1,1) = 2;
(*A)(1,2) = 1;
(*A)(2,0) = 3;
(*A)(2,1) = 2;
(*A)(2,2) = 2;
(*A)(3,0) = -3;
(*A)(3,1) = 8;
(*A)(3,2) = 5;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 2;
(*b)[1] = 4;
(*b)[2] = 5;
(*b)[3] = 17;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There should be an exact solution as even though the system is overdetermined but
//as the Rank is 3 and the amount of unknowns is 3
std::cout << "============== Test 9 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,4);
(*A)(0,0) = 1;
(*A)(0,1) = 3;
(*A)(0,2) = 1;
(*A)(0,3) = 1;
(*A)(1,0) = 2;
(*A)(1,1) = -2;
(*A)(1,2) = 1;
(*A)(1,3) = 2;
(*A)(2,0) = 1;
(*A)(2,1) = -5;
(*A)(2,2) = 0;
(*A)(2,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 3;
(*b)[1] = 8;
(*b)[2] = 5;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//It is an undetermined system, so no exact solution as it has free variables
std::cout << "============== Test 10 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,4);
(*A)(0,0) = 1;
(*A)(0,1) = 0;
(*A)(0,2) = 0;
(*A)(0,3) = 1;
(*A)(1,0) = 0;
(*A)(1,1) = 1;
(*A)(1,2) = 0;
(*A)(1,3) = 1;
(*A)(2,0) = 0;
(*A)(2,1) = 0;
(*A)(2,2) = 1;
(*A)(2,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 1;
(*b)[1] = 1;
(*b)[2] = 1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 11 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 1;
(*A)(0,3) = -1;
(*A)(1,0) = -1;
(*A)(1,1) = 1;
(*A)(1,2) = -1;
(*A)(1,3) = 1;
(*A)(2,0) = 1;
(*A)(2,1) = -1;
(*A)(2,2) = 1;
(*A)(2,3) = -1;
(*A)(3,0) = -1;
(*A)(3,1) = 1;
(*A)(3,2) = -1;
(*A)(3,3) = 1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
(*b)[3] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//It is an underdetermined system, so no exact solution as it has free variables
//fails here though because no pivoting is done
std::cout << "============== Test 12 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = 2;
(*A)(0,2) = 3;
(*A)(1,0) = 4;
(*A)(1,1) = 5;
(*A)(1,2) = 6;
(*A)(2,0) = 7;
(*A)(2,1) = 8;
(*A)(2,2) = 9;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 0;
(*b)[1] = 0;
(*b)[2] = 0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//There shouldn't be an exact solution as it has free variables
std::cout << "============== Test 13 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 2;
(*A)(1,0) = 0;
(*A)(1,1) = 0;
(*A)(1,2) = -1;
(*A)(2,0) = 0;
(*A)(2,1) = 2;
(*A)(2,2) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -11;
(*b)[2] = -3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Should gave the same result as test 14 if pivoting has been implemented correctly
std::cout << "============== Test 14 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
(*A)(0,0) = 1;
(*A)(0,1) = -1;
(*A)(0,2) = 2;
(*A)(1,0) = 0;
(*A)(1,1) = 2;
(*A)(1,2) = -1;
(*A)(2,0) = 0;
(*A)(2,1) = 0;
(*A)(2,2) = -1;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
(*b)[0] = 8;
(*b)[1] = -3;
(*b)[2] = -11;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
//Same system of equations as test 13*/
std::cout << "============== Test 15 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
(*A)(0,0) = A10;
(*A)(0,1) = A11;
(*A)(1,0) = A00;
(*A)(1,1) = A01;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
(*b)[0] = B1;
(*b)[1] = B0;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 16 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(3,4);
A01.assign(1,2);
A10.assign(0,1);
A11.assign(7,8);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,4);
B1.assign(-1,1);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 17 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,4);
A01.assign(8,10);
A10.assign(2,4);
A11.assign(4,6);
(*A)(0,0) = -A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(4,6);
B1.assign(8,10);
(*b)[0] = -B0;
(*b)[1] = -B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 18 ==============" << std::endl << std::endl;
A = new DoubleMatrix(4,4);
A00.assign(4,6);
A01.assign(-6,-4);
A10.assign(9,11);
A11.assign(-11,-9);
DoubleInterval A33(-1,1);
(*A)(0,0) = A00;
(*A)(0,1) = A33;
(*A)(0,2) = A33;
(*A)(0,3) = A33;
(*A)(1,0) = A33;
(*A)(1,1) = A01;
(*A)(1,2) = A33;
(*A)(1,3) = A33;
(*A)(2,0) = A33;
(*A)(2,1) = A33;
(*A)(2,2) = A10;
(*A)(2,3) = A33;
(*A)(3,0) = A33;
(*A)(3,1) = A33;
(*A)(3,2) = A33;
(*A)(3,3) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(4, (DoubleInterval)0);
B0.assign(-2,4);
B1.assign(1,8);
DoubleInterval B2(-4,10);
DoubleInterval B3(2,12);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
(*b)[3] = B3;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(4, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 19 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,14);
B1.assign(-9,9);
B2.assign(-3,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 20 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(-14,0);
B1.assign(-9,0);
B2.assign(-3,0);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 21 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(0,14);
B1.assign(0,9);
B2.assign(0,3);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 22 ==============" << std::endl << std::endl;
A = new DoubleMatrix(3,3);
A00.assign(3.7, 4.3);
A01.assign(-1.5, -0.5);
A10.assign(3.7, 4.3);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(0,2) = (DoubleInterval)0;
(*A)(1,0) = A01;
(*A)(1,1) = A10;
(*A)(1,2) = A01;
(*A)(2,0) = (DoubleInterval)0;
(*A)(2,1) = A01;
(*A)(2,2) = A10;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(3, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(-9,-3);
B2.assign(-3,1);
(*b)[0] = B0;
(*b)[1] = B1;
(*b)[2] = B2;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(3, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
std::cout << "============== Test 23 ==============" << std::endl << std::endl;
A = new DoubleMatrix(2,2);
A00.assign(2,3);
A01.assign(-1,1);
A10.assign(0,5);
A11.assign(3,4);
(*A)(0,0) = A00;
(*A)(0,1) = A01;
(*A)(1,0) = A10;
(*A)(1,1) = A11;
std::cout << "A = " << std::endl;
std::cout << *A << std::endl;
b = new DoubleVector(2, (DoubleInterval)0);
B0.assign(2,14);
B1.assign(3,9);
(*b)[0] = B0;
(*b)[1] = B1;
std::cout << "b = " << std::endl;
std::cout << *b << std::endl << std::endl;
x = new DoubleVector(2, (DoubleInterval)0);
try
{
x = hansen_gaussian_elimination_v1(*A,*b);
if(x != NULL)
{
std::cout << "x = " << std::endl;
std::cout << *x << std::endl << std::endl;
}
}
catch(const std::exception& e)
{
std::cout << e.what() << std::endl << std::endl;
}
catch(std::string& error)
{
std::cout << error << std::endl << std::endl;
}
delete A;
delete b;
delete x;
return 0;
}
inline void
TwoSidedTrsmLVar2
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmLVar2");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( L.Height() != L.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != L.Height() )
throw std::logic_error("A and L must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
// Temporary distributions
DistMatrix<F,MR, STAR> A10Adj_MR_STAR(g);
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MR, STAR> F10Adj_MR_STAR(g);
DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g);
DistMatrix<F,VC, STAR> L10Adj_VC_STAR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,MC, STAR> X11_MC_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(g);
DistMatrix<F,MC, STAR> Y10Adj_MC_STAR(g);
DistMatrix<F,MR, MC > Y10Adj_MR_MC(g);
DistMatrix<F> X11(g);
DistMatrix<F> Y10Adj(g);
Matrix<F> Y10Local;
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A10Adj_MR_STAR.AlignWith( L10 );
F10Adj_MR_STAR.AlignWith( A00 );
L10Adj_MR_STAR.AlignWith( A00 );
L10Adj_VC_STAR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
X11.AlignWith( A11 );
X11_MC_STAR.AlignWith( L10 );
X21_MC_STAR.AlignWith( A20 );
Y10Adj_MC_STAR.AlignWith( A00 );
Y10Adj_MR_MC.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := L10 A00
L10Adj_MR_STAR.AdjointFrom( L10 );
L10Adj_VC_STAR = L10Adj_MR_STAR;
L10_STAR_MC.AdjointFrom( L10Adj_VC_STAR );
Y10Adj_MC_STAR.ResizeTo( A10.Width(), A10.Height() );
F10Adj_MR_STAR.ResizeTo( A10.Width(), A10.Height() );
Zero( Y10Adj_MC_STAR );
Zero( F10Adj_MR_STAR );
LocalSymmetricAccumulateRL
( ADJOINT,
F(1), A00, L10_STAR_MC, L10Adj_MR_STAR,
Y10Adj_MC_STAR, F10Adj_MR_STAR );
Y10Adj.SumScatterFrom( Y10Adj_MC_STAR );
Y10Adj_MR_MC = Y10Adj;
Y10Adj_MR_MC.SumScatterUpdate( F(1), F10Adj_MR_STAR );
Adjoint( Y10Adj_MR_MC.LockedLocalMatrix(), Y10Local );
// X11 := A10 L10'
X11_MC_STAR.ResizeTo( A11.Height(), A11.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A10, L10Adj_MR_STAR, F(0), X11_MC_STAR );
// A10 := A10 - Y10
Axpy( F(-1), Y10Local, A10.LocalMatrix() );
A10Adj_MR_STAR.AdjointFrom( A10 );
// A11 := A11 - (X11 + L10 A10') = A11 - (A10 L10' + L10 A10')
LocalGemm
( NORMAL, NORMAL, F(1), L10, A10Adj_MR_STAR, F(1), X11_MC_STAR );
X11.SumScatterFrom( X11_MC_STAR );
MakeTrapezoidal( LEFT, LOWER, 0, X11 );
Axpy( F(-1), X11, A11 );
// A10 := inv(L11) A10
L11_STAR_STAR = L11;
A10_STAR_VR.AdjointFrom( A10Adj_MR_STAR );
LocalTrsm
( LEFT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A11 := inv(L11) A11 inv(L11)'
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 - A20 L10'
X21_MC_STAR.ResizeTo( A21.Height(), A21.Width() );
LocalGemm
( NORMAL, NORMAL, F(1), A20, L10Adj_MR_STAR, F(0), X21_MC_STAR );
A21.SumScatterUpdate( F(-1), X21_MC_STAR );
// A21 := A21 inv(L11)'
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10Adj_MR_STAR.FreeAlignments();
F10Adj_MR_STAR.FreeAlignments();
L10Adj_MR_STAR.FreeAlignments();
L10Adj_VC_STAR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
X11.FreeAlignments();
X11_MC_STAR.FreeAlignments();
X21_MC_STAR.FreeAlignments();
Y10Adj_MC_STAR.FreeAlignments();
Y10Adj_MR_MC.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/**********************************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
int main()
{
DoubleMatrix X(3,3);
DoubleInterval A(2,5);
X = A;
DoubleMatrix Y(3,3);
DoubleInterval B(5,9);
Y = B;
std::cout << X << std::endl;
std::cout << Y << std::endl;
DoubleMatrix Z(3,3);
Z = mtl::mat::trans(X);
std::cout << Z << std::endl;
mtl::mat::swap_row(Z,1,2);
std::cout << Z << std::endl;
DoubleInterval C;
C = boost::numeric::max(A,B);
std::cout << C << std::endl;
std::cout << "============== Test 1 ==============" << std::endl << std::endl;
DoubleInterval A00(2,3);
DoubleInterval A01(0,1);
DoubleInterval A10(1,2);
DoubleInterval A11(2,3);
DoubleMatrix *Test = new DoubleMatrix(2,2);
(*Test)(0,0) = A00;
(*Test)(0,1) = A01;
(*Test)(1,0) = A10;
(*Test)(1,1) = A11;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
bool diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
std::cout << "Max on row 2 is " << row_max_element(*Test,1,0) << std::endl;
std::cout << "The max is located on element " << row_max_term(*Test,1,0) << std::endl;
std::cout << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 2 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(3,3);
(*Test)(0,0) = 1;
(*Test)(0,1) = 2;
(*Test)(0,2) = 3;
(*Test)(1,0) = 4;
(*Test)(1,1) = 5;
(*Test)(1,2) = 6;
(*Test)(2,0) = 7;
(*Test)(2,1) = 8;
(*Test)(2,2) = 9;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
for(unsigned int i = 0; i < mtl::mat::num_rows(*Test); i++)
{
std::cout << "Max on row " << i << " is " << row_max_element(*Test,i,0) << std::endl;
std::cout << "The max is located on element " << row_max_term(*Test,i,0) << std::endl;
}
std::cout << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 3 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(3,3);
(*Test)(0,0) = 1;
(*Test)(0,1) = 2;
(*Test)(0,2) = 3;
(*Test)(1,0) = 10;
(*Test)(1,1) = 5;
(*Test)(1,2) = 6;
(*Test)(2,0) = 10;
(*Test)(2,1) = 8;
(*Test)(2,2) = 9;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
for(unsigned int i = 0; i < mtl::mat::num_cols(*Test); i++)
{
std::cout << "Max on col " << i << " is " << col_max_element(*Test,i,0) << std::endl;
std::cout << "The max is located on element " << col_max_term(*Test,i,0) << std::endl;
}
std::cout << std::endl;
std::cout << "DoubleMatrix minor(1,0) = " << std::endl;
std::cout << matrix_minor(*Test,1,0) << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
std::cout << "============== Test 4 ==============" << std::endl << std::endl;
Test = new DoubleMatrix(2,2);
(*Test)(0,0) = A10;
(*Test)(0,1) = A11;
(*Test)(1,0) = A00;
(*Test)(1,1) = A01;
std::cout << "Test: " << std::endl;
std::cout << *Test << std::endl;
diag = diagonally_dominant(*Test);
if(diag == true)
std::cout << "Test is diagonally dominant" << std::endl << std::endl;
else
std::cout << "Test is NOT diagonally dominant" << std::endl << std::endl;
std::cout << "The midpoint Doublematrix m(Test): " << std::endl;
std::cout << m(*Test) << std::endl;
std::cout << "determinant = " << det(*Test) << std::endl;
delete Test;
return 0;
}
void LSquare
( DistMatrix<Complex<R> >& A,
DistMatrix<Complex<R>,STAR,STAR>& t )
{
#ifndef RELEASE
CallStackEntry entry("hermitian_tridiag::LSquare");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
const Grid& g = A.Grid();
#ifndef RELEASE
if( g.Height() != g.Width() )
throw std::logic_error("The process grid must be square");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( t.Viewing() )
throw std::logic_error("t must not be a view");
#endif
typedef Complex<R> C;
DistMatrix<C,MD,STAR> tDiag(g);
tDiag.AlignWithDiagonal( A, -1 );
tDiag.ResizeTo( A.Height()-1, 1 );
// Matrix views
DistMatrix<C>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<C,MD,STAR> tT(g), t0(g),
tB(g), t1(g),
t2(g);
// Temporary distributions
DistMatrix<C> WPan(g);
DistMatrix<C,STAR,STAR> t1_STAR_STAR(g);
DistMatrix<C,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<C,MC, STAR> APan_MC_STAR(g), A11_MC_STAR(g),
A21_MC_STAR(g);
DistMatrix<C,MR, STAR> APan_MR_STAR(g), A11_MR_STAR(g),
A21_MR_STAR(g);
DistMatrix<C,MC, STAR> WPan_MC_STAR(g), W11_MC_STAR(g),
W21_MC_STAR(g);
DistMatrix<C,MR, STAR> WPan_MR_STAR(g), W11_MR_STAR(g),
W21_MR_STAR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( tDiag, tT,
tB, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
if( A22.Height() > 0 )
{
WPan.AlignWith( A11 );
APan_MC_STAR.AlignWith( A11 );
WPan_MC_STAR.AlignWith( A11 );
APan_MR_STAR.AlignWith( A11 );
WPan_MR_STAR.AlignWith( A11 );
//----------------------------------------------------------------//
WPan.ResizeTo( ABR.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
hermitian_tridiag::PanelLSquare
( ABR, WPan, t1,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionDown
( APan_MC_STAR, A11_MC_STAR,
A21_MC_STAR, A11.Height() );
PartitionDown
( APan_MR_STAR, A11_MR_STAR,
A21_MR_STAR, A11.Height() );
PartitionDown
( WPan_MC_STAR, W11_MC_STAR,
W21_MC_STAR, A11.Height() );
PartitionDown
( WPan_MR_STAR, W11_MR_STAR,
W21_MR_STAR, A11.Height() );
LocalTrr2k
( LOWER, ADJOINT, ADJOINT,
C(-1), A21_MC_STAR, W21_MR_STAR,
W21_MC_STAR, A21_MR_STAR,
C(1), A22 );
//----------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
t1_STAR_STAR.ResizeTo( t1.Height(), 1 );
HermitianTridiag
( LOWER, A11_STAR_STAR.Matrix(), t1_STAR_STAR.Matrix() );
A11 = A11_STAR_STAR;
t1 = t1_STAR_STAR;
}
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
// Redistribute from matrix-diagonal form to fully replicated
t = tDiag;
}
void LSquare( DistMatrix<R>& A )
{
#ifndef RELEASE
CallStackEntry entry("hermitian_tridiag::LSquare");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( A.Grid().Height() != A.Grid().Width() )
throw std::logic_error("The process grid must be square");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<R>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<R> WPan(g);
DistMatrix<R,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<R,MC, STAR> APan_MC_STAR(g), A11_MC_STAR(g),
A21_MC_STAR(g);
DistMatrix<R,MR, STAR> APan_MR_STAR(g), A11_MR_STAR(g),
A21_MR_STAR(g);
DistMatrix<R,MC, STAR> WPan_MC_STAR(g), W11_MC_STAR(g),
W21_MC_STAR(g);
DistMatrix<R,MR, STAR> WPan_MR_STAR(g), W11_MR_STAR(g),
W21_MR_STAR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
if( A22.Height() > 0 )
{
WPan.AlignWith( A11 );
APan_MC_STAR.AlignWith( A11 );
WPan_MC_STAR.AlignWith( A11 );
APan_MR_STAR.AlignWith( A11 );
WPan_MR_STAR.AlignWith( A11 );
//----------------------------------------------------------------//
WPan.ResizeTo( ABR.Height(), A11.Width() );
APan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MC_STAR.ResizeTo( ABR.Height(), A11.Width() );
APan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
WPan_MR_STAR.ResizeTo( ABR.Height(), A11.Width() );
hermitian_tridiag::PanelLSquare
( ABR, WPan,
APan_MC_STAR, APan_MR_STAR, WPan_MC_STAR, WPan_MR_STAR );
PartitionDown
( APan_MC_STAR, A11_MC_STAR,
A21_MC_STAR, A11.Height() );
PartitionDown
( APan_MR_STAR, A11_MR_STAR,
A21_MR_STAR, A11.Height() );
PartitionDown
( WPan_MC_STAR, W11_MC_STAR,
W21_MC_STAR, A11.Height() );
PartitionDown
( WPan_MR_STAR, W11_MR_STAR,
W21_MR_STAR, A11.Height() );
LocalTrr2k
( LOWER, TRANSPOSE, TRANSPOSE,
R(-1), A21_MC_STAR, W21_MR_STAR,
W21_MC_STAR, A21_MR_STAR,
R(1), A22 );
//----------------------------------------------------------------//
WPan_MR_STAR.FreeAlignments();
APan_MR_STAR.FreeAlignments();
WPan_MC_STAR.FreeAlignments();
APan_MC_STAR.FreeAlignments();
WPan.FreeAlignments();
}
else
{
A11_STAR_STAR = A11;
HermitianTridiag( LOWER, A11_STAR_STAR.Matrix() );
A11 = A11_STAR_STAR;
}
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
internal::CholeskyUVar3Square( DistMatrix<F,MC,MR>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyUVar3Square");
if( A.Height() != A.Width() )
throw std::logic_error
("Can only compute Cholesky factor of square matrices.");
if( A.Grid().Height() != A.Grid().Width() )
throw std::logic_error
("CholeskyUVar3Square assumes a square process grid.");
#endif
const Grid& g = A.Grid();
// Find the process holding our transposed data
const int r = g.Height();
int transposeRank;
{
const int colAlignment = A.ColAlignment();
const int rowAlignment = A.RowAlignment();
const int colShift = A.ColShift();
const int rowShift = A.RowShift();
const int transposeRow = (colAlignment+rowShift) % r;
const int transposeCol = (rowAlignment+colShift) % r;
transposeRank = transposeRow + r*transposeCol;
}
const bool onDiagonal = ( transposeRank == g.VCRank() );
// Matrix views
DistMatrix<F,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary matrix distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
internal::LocalCholesky( UPPER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A12_STAR_VR = A12;
internal::LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, (F)1, A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
// SendRecv to form A12[* ,MC] from A12[* ,MR]
A12_STAR_MC.ResizeTo( A12.Height(), A12.Width() );
{
if( onDiagonal )
{
const int size = A11.Height()*A22.LocalWidth();
MemCopy
( A12_STAR_MC.LocalBuffer(),
A12_STAR_MR.LocalBuffer(), size );
}
else
{
const int sendSize = A11.Height()*A22.LocalWidth();
const int recvSize = A11.Width()*A22.LocalHeight();
// We know that the ldim is the height since we have manually
// created both temporary matrices.
mpi::SendRecv
( A12_STAR_MR.LocalBuffer(), sendSize, transposeRank, 0,
A12_STAR_MC.LocalBuffer(), recvSize, transposeRank, 0,
g.VCComm() );
}
}
internal::LocalTrrk
( UPPER, ADJOINT, (F)-1, A12_STAR_MC, A12_STAR_MR, (F)1, A22 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrmmUVar5");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( U.Height() != U.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != U.Height() )
throw std::logic_error("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,MC, STAR> A01_MC_STAR(g);
DistMatrix<F,MR, STAR> A01_MR_STAR(g);
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MC, STAR> U01_MC_STAR(g);
DistMatrix<F,MR, STAR> U01_MR_STAR(g);
DistMatrix<F,VC, STAR> U01_VC_STAR(g);
DistMatrix<F,VC, STAR> Y01_VC_STAR(g);
DistMatrix<F> Y01(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A01_MC_STAR.AlignWith( A00 );
A01_MR_STAR.AlignWith( A00 );
A01_VC_STAR.AlignWith( A00 );
U01_MC_STAR.AlignWith( A00 );
U01_MR_STAR.AlignWith( A00 );
U01_VC_STAR.AlignWith( A00 );
Y01.AlignWith( A01 );
Y01_VC_STAR.AlignWith( A01 );
//--------------------------------------------------------------------//
// Y01 := U01 A11
A11_STAR_STAR = A11;
U01_VC_STAR = U01;
Y01_VC_STAR.ResizeTo( A01.Height(), A01.Width() );
Hemm
( RIGHT, UPPER,
F(1), A11_STAR_STAR.LocalMatrix(), U01_VC_STAR.LocalMatrix(),
F(0), Y01_VC_STAR.LocalMatrix() );
Y01 = Y01_VC_STAR;
// A01 := U00 A01
Trmm( LEFT, UPPER, NORMAL, diag, F(1), U00, A01 );
// A01 := A01 + 1/2 Y01
Axpy( F(1)/F(2), Y01, A01 );
// A00 := A00 + (U01 A01' + A01 U01')
A01_MC_STAR = A01;
U01_MC_STAR = U01;
A01_VC_STAR = A01_MC_STAR;
A01_MR_STAR = A01_VC_STAR;
U01_MR_STAR = U01_MC_STAR;
LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
F(1), U01_MC_STAR, A01_MR_STAR,
A01_MC_STAR, U01_MR_STAR,
F(1), A00 );
// A01 := A01 + 1/2 Y01
Axpy( F(1)/F(2), Y01_VC_STAR, A01_VC_STAR );
// A01 := A01 U11'
U11_STAR_STAR = U11;
LocalTrmm
( RIGHT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
// A11 := U11 A11 U11'
LocalTwoSidedTrmm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
//--------------------------------------------------------------------//
A01_MC_STAR.FreeAlignments();
A01_MR_STAR.FreeAlignments();
A01_VC_STAR.FreeAlignments();
U01_MC_STAR.FreeAlignments();
U01_MR_STAR.FreeAlignments();
U01_VC_STAR.FreeAlignments();
Y01.FreeAlignments();
Y01_VC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
internal::HegstLLVar4( DistMatrix<F,MC,MR>& A, const DistMatrix<F,MC,MR>& L )
{
#ifndef RELEASE
PushCallStack("internal::HegstLLVar4");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( L.Height() != L.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != L.Height() )
throw std::logic_error("A and L must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F,MC,MR>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
// Temporary distributions
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,MC > A10_STAR_MC(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,STAR,VR > L10_STAR_VR(g);
DistMatrix<F,STAR,MR > L10_STAR_MR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,VR > Y10_STAR_VR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A10_STAR_VR.AlignWith( A00 );
A10_STAR_MR.AlignWith( A00 );
A10_STAR_MC.AlignWith( A00 );
A21_MC_STAR.AlignWith( A20 );
L10_STAR_VR.AlignWith( A00 );
L10_STAR_MR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
Y10_STAR_VR.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := A11 L10
A11_STAR_STAR = A11;
L10_STAR_VR = L10;
Y10_STAR_VR.ResizeTo( A10.Height(), A10.Width() );
Zero( Y10_STAR_VR );
Hemm
( LEFT, LOWER,
(F)0.5, A11_STAR_STAR.LockedLocalMatrix(),
L10_STAR_VR.LockedLocalMatrix(),
(F)0, Y10_STAR_VR.LocalMatrix() );
// A10 := A10 + 1/2 Y10
A10_STAR_VR = A10;
Axpy( (F)1, Y10_STAR_VR, A10_STAR_VR );
// A00 := A00 + (A10' L10 + L10' A10)
A10_STAR_MR = A10_STAR_VR;
A10_STAR_MC = A10_STAR_VR;
L10_STAR_MR = L10_STAR_VR;
L10_STAR_MC = L10_STAR_VR;
internal::LocalTrr2k
( LOWER, ADJOINT, ADJOINT,
(F)1, A10_STAR_MC, L10_STAR_MR,
L10_STAR_MC, A10_STAR_MR,
(F)1, A00 );
// A10 := A10 + 1/2 Y10
Axpy( (F)1, Y10_STAR_VR, A10_STAR_VR );
// A10 := L11' A10
L11_STAR_STAR = L11;
internal::LocalTrmm
( LEFT, LOWER, ADJOINT, NON_UNIT, (F)1, L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A20 := A20 + A21 L10
A21_MC_STAR = A21;
internal::LocalGemm
( NORMAL, NORMAL, (F)1, A21_MC_STAR, L10_STAR_MR, (F)1, A20 );
// A11 := L11' A11 L11
internal::LocalHegst
( LEFT, LOWER, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 L11
A21_VC_STAR = A21_MC_STAR;
internal::LocalTrmm
( RIGHT, LOWER, NORMAL, NON_UNIT, (F)1, L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10_STAR_VR.FreeAlignments();
A10_STAR_MR.FreeAlignments();
A10_STAR_MC.FreeAlignments();
A21_MC_STAR.FreeAlignments();
L10_STAR_VR.FreeAlignments();
L10_STAR_MR.FreeAlignments();
L10_STAR_MC.FreeAlignments();
Y10_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LQ( DistMatrix<Complex<R>,MC,MR >& A,
DistMatrix<Complex<R>,MD,STAR>& t )
{
#ifndef RELEASE
PushCallStack("LQ");
if( A.Grid() != t.Grid() )
throw std::logic_error("{A,t} must be distributed over the same grid");
#endif
typedef Complex<R> C;
const Grid& g = A.Grid();
if( t.Viewing() )
{
if( !t.AlignedWithDiagonal( A ) )
throw std::logic_error("t was not aligned with A");
if( t.Height() != std::min(A.Height(),A.Width()) || t.Width() != 1 )
throw std::logic_error("t was not the appropriate shape");
}
else
{
t.AlignWithDiagonal( A );
t.ResizeTo( std::min(A.Height(),A.Width()), 1 );
}
// Matrix views
DistMatrix<C,MC,MR>
ATL(g), ATR(g), A00(g), A01(g), A02(g), ATopPan(g), ABottomPan(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<C,MD,STAR>
tT(g), t0(g),
tB(g), t1(g),
t2(g);
PartitionDownLeftDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( t, tT,
tB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( tT, t0,
/**/ /**/
t1,
tB, t2 );
ATopPan.View1x2( A11, A12 );
ABottomPan.View1x2( A21, A22 );
//--------------------------------------------------------------------//
internal::PanelLQ( ATopPan, t1 );
ApplyPackedReflectors
( RIGHT, UPPER, HORIZONTAL, FORWARD, CONJUGATED,
0, ATopPan, t1, ABottomPan );
//--------------------------------------------------------------------//
SlidePartitionDown
( tT, t0,
t1,
/**/ /**/
tB, t2 );
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrsmUVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrsmUVar4");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( U.Height() != U.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != U.Height() )
LogicError("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,VC, STAR> A01_VC_STAR(g);
DistMatrix<F,STAR,MC > A01Trans_STAR_MC(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,VC > A12_STAR_VC(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,MR, STAR> U12Trans_MR_STAR(g);
DistMatrix<F,VR, STAR> U12Trans_VR_STAR(g);
DistMatrix<F,STAR,VR > U12_STAR_VR(g);
DistMatrix<F,STAR,VC > U12_STAR_VC(g);
DistMatrix<F,STAR,MC > U12_STAR_MC(g);
DistMatrix<F,STAR,VR > Y12_STAR_VR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A01_VC_STAR.AlignWith( A02 );
A01Trans_STAR_MC.AlignWith( A02 );
A12_STAR_VR.AlignWith( A22 );
A12_STAR_VC.AlignWith( A22 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
U12Trans_MR_STAR.AlignWith( A02 );
U12Trans_VR_STAR.AlignWith( A02 );
U12_STAR_VR.AlignWith( A02 );
U12_STAR_VC.AlignWith( A22 );
U12_STAR_MC.AlignWith( A22 );
Y12_STAR_VR.AlignWith( A12 );
//--------------------------------------------------------------------//
// A01 := A01 inv(U11)
A01_VC_STAR = A01;
U11_STAR_STAR = U11;
LocalTrsm
( RIGHT, UPPER, NORMAL, diag, F(1), U11_STAR_STAR, A01_VC_STAR );
A01 = A01_VC_STAR;
// A11 := inv(U11)' A11 inv(U11)
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// A02 := A02 - A01 U12
A01Trans_STAR_MC.TransposeFrom( A01_VC_STAR );
U12Trans_MR_STAR.TransposeFrom( U12 );
LocalGemm
( TRANSPOSE, TRANSPOSE,
F(-1), A01Trans_STAR_MC, U12Trans_MR_STAR, F(1), A02 );
// Y12 := A11 U12
U12Trans_VR_STAR = U12Trans_MR_STAR;
Zeros( U12_STAR_VR, A12.Height(), A12.Width() );
Transpose( U12Trans_VR_STAR.Matrix(), U12_STAR_VR.Matrix() );
Zeros( Y12_STAR_VR, A12.Height(), A12.Width() );
Hemm
( LEFT, UPPER,
F(1), A11_STAR_STAR.Matrix(), U12_STAR_VR.Matrix(),
F(0), Y12_STAR_VR.Matrix() );
// A12 := inv(U11)' A12
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12_STAR_VR, A12_STAR_VR );
// A22 := A22 - (A12' U12 + U12' A12)
A12_STAR_MR = A12_STAR_VR;
A12_STAR_VC = A12_STAR_VR;
U12_STAR_VC = U12_STAR_VR;
A12_STAR_MC = A12_STAR_VC;
U12_STAR_MC = U12_STAR_VC;
LocalTrr2k
( UPPER, ADJOINT, TRANSPOSE, ADJOINT,
F(-1), A12_STAR_MC, U12Trans_MR_STAR,
U12_STAR_MC, A12_STAR_MR,
F(1), A22 );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12_STAR_VR, A12_STAR_VR );
A12 = A12_STAR_VR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/**********************************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
}
inline void
LocalSymmetricAccumulateLU
( Orientation orientation, T alpha,
const DistMatrix<T>& A,
const DistMatrix<T,MC, STAR>& B_MC_STAR,
const DistMatrix<T,STAR,MR >& BAdjOrTrans_STAR_MR,
DistMatrix<T,MC, STAR>& Z_MC_STAR,
DistMatrix<T,MR, STAR>& Z_MR_STAR )
{
#ifndef RELEASE
PushCallStack("internal::LocalSymmetricAccumulateLU");
if( A.Grid() != B_MC_STAR.Grid() ||
B_MC_STAR.Grid() != BAdjOrTrans_STAR_MR.Grid() ||
BAdjOrTrans_STAR_MR.Grid() != Z_MC_STAR.Grid() ||
Z_MC_STAR.Grid() != Z_MR_STAR.Grid() )
throw std::logic_error
("{A,B,Z} must be distributed over the same grid");
if( A.Height() != A.Width() ||
A.Height() != B_MC_STAR.Height() ||
A.Height() != BAdjOrTrans_STAR_MR.Width() ||
A.Height() != Z_MC_STAR.Height() ||
A.Height() != Z_MR_STAR.Height() ||
B_MC_STAR.Width() != BAdjOrTrans_STAR_MR.Height() ||
BAdjOrTrans_STAR_MR.Height() != Z_MC_STAR.Width() ||
Z_MC_STAR.Width() != Z_MR_STAR.Width() )
{
std::ostringstream msg;
msg << "Nonconformal LocalSymmetricAccumulateLU: \n"
<< " A ~ " << A.Height() << " x " << A.Width() << "\n"
<< " B[MC,* ] ~ " << B_MC_STAR.Height() << " x "
<< B_MC_STAR.Width() << "\n"
<< " B^H/T[* ,MR] ~ " << BAdjOrTrans_STAR_MR.Height() << " x "
<< BAdjOrTrans_STAR_MR.Width() << "\n"
<< " Z[MC,* ] ~ " << Z_MC_STAR.Height() << " x "
<< Z_MC_STAR.Width() << "\n"
<< " Z[MR,* ] ` " << Z_MR_STAR.Height() << " x "
<< Z_MR_STAR.Width() << "\n";
throw std::logic_error( msg.str().c_str() );
}
if( B_MC_STAR.ColAlignment() != A.ColAlignment() ||
BAdjOrTrans_STAR_MR.RowAlignment() != A.RowAlignment() ||
Z_MC_STAR.ColAlignment() != A.ColAlignment() ||
Z_MR_STAR.ColAlignment() != A.RowAlignment() )
throw std::logic_error("Partial matrix distributions are misaligned");
#endif
const Grid& g = A.Grid();
DistMatrix<T>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<T> D11(g);
DistMatrix<T,MC,STAR>
BT_MC_STAR(g), B0_MC_STAR(g),
BB_MC_STAR(g), B1_MC_STAR(g),
B2_MC_STAR(g);
DistMatrix<T,STAR,MR>
BLAdjOrTrans_STAR_MR(g), BRAdjOrTrans_STAR_MR(g),
B0AdjOrTrans_STAR_MR(g), B1AdjOrTrans_STAR_MR(g),
B2AdjOrTrans_STAR_MR(g);
DistMatrix<T,MC,STAR>
ZT_MC_STAR(g), Z0_MC_STAR(g),
ZB_MC_STAR(g), Z1_MC_STAR(g),
Z2_MC_STAR(g);
DistMatrix<T,MR,STAR>
ZT_MR_STAR(g), Z0_MR_STAR(g),
ZB_MR_STAR(g), Z1_MR_STAR(g),
Z2_MR_STAR(g);
const int ratio = std::max( g.Height(), g.Width() );
PushBlocksizeStack( ratio*Blocksize() );
LockedPartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDown
( B_MC_STAR, BT_MC_STAR,
BB_MC_STAR, 0 );
LockedPartitionRight
( BAdjOrTrans_STAR_MR, BLAdjOrTrans_STAR_MR, BRAdjOrTrans_STAR_MR, 0 );
PartitionDown
( Z_MC_STAR, ZT_MC_STAR,
ZB_MC_STAR, 0 );
PartitionDown
( Z_MR_STAR, ZT_MR_STAR,
ZB_MR_STAR, 0 );
while( ATL.Height() < A.Height() )
{
LockedRepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDown
( BT_MC_STAR, B0_MC_STAR,
/**********/ /**********/
B1_MC_STAR,
BB_MC_STAR, B2_MC_STAR );
LockedRepartitionRight
( BLAdjOrTrans_STAR_MR, /**/ BRAdjOrTrans_STAR_MR,
B0AdjOrTrans_STAR_MR, /**/ B1AdjOrTrans_STAR_MR,
B2AdjOrTrans_STAR_MR );
RepartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
/**********/ /**********/
Z1_MC_STAR,
ZB_MC_STAR, Z2_MC_STAR );
RepartitionDown
( ZT_MR_STAR, Z0_MR_STAR,
/**********/ /**********/
Z1_MR_STAR,
ZB_MR_STAR, Z2_MR_STAR );
D11.AlignWith( A11 );
//--------------------------------------------------------------------//
D11 = A11;
MakeTrapezoidal( LEFT, UPPER, 0, D11 );
LocalGemm
( NORMAL, orientation,
alpha, D11, B1AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
MakeTrapezoidal( LEFT, UPPER, 1, D11 );
LocalGemm
( orientation, NORMAL, alpha, D11, B1_MC_STAR, T(1), Z1_MR_STAR );
LocalGemm
( NORMAL, orientation,
alpha, A12, B2AdjOrTrans_STAR_MR, T(1), Z1_MC_STAR );
LocalGemm
( orientation, NORMAL, alpha, A12, B1_MC_STAR, T(1), Z2_MR_STAR );
//--------------------------------------------------------------------//
D11.FreeAlignments();
SlideLockedPartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDown
( BT_MC_STAR, B0_MC_STAR,
B1_MC_STAR,
/**********/ /**********/
BB_MC_STAR, B2_MC_STAR );
SlideLockedPartitionRight
( BLAdjOrTrans_STAR_MR, /**/ BRAdjOrTrans_STAR_MR,
B0AdjOrTrans_STAR_MR, B1AdjOrTrans_STAR_MR, /**/ B2AdjOrTrans_STAR_MR );
SlidePartitionDown
( ZT_MC_STAR, Z0_MC_STAR,
Z1_MC_STAR,
/**********/ /**********/
ZB_MC_STAR, Z2_MC_STAR );
SlidePartitionDown
( ZT_MR_STAR, Z0_MR_STAR,
Z1_MR_STAR,
/**********/ /**********/
ZB_MR_STAR, Z2_MR_STAR );
}
PopBlocksizeStack();
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LU( DistMatrix<F>& A, DistMatrix<int,VC,STAR>& p )
{
#ifndef RELEASE
CallStackEntry entry("LU");
if( A.Grid() != p.Grid() )
throw std::logic_error("{A,p} must be distributed over the same grid");
if( p.Viewing() &&
(std::min(A.Height(),A.Width()) != p.Height() || p.Width() != 1) )
throw std::logic_error
("p must be a vector of the same height as the min dimension of A.");
#endif
const Grid& g = A.Grid();
if( !p.Viewing() )
p.ResizeTo( std::min(A.Height(),A.Width()), 1 );
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g), AB(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<int,VC,STAR>
pT(g), p0(g),
pB(g), p1(g),
p2(g);
// Temporary distributions
DistMatrix<F, STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F, MC, STAR> A21_MC_STAR(g);
DistMatrix<F, STAR,VR > A12_STAR_VR(g);
DistMatrix<F, STAR,MR > A12_STAR_MR(g);
DistMatrix<int,STAR,STAR> p1_STAR_STAR(g);
// Pivot composition
std::vector<int> image, preimage;
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
PartitionDown
( p, pT,
pB, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
RepartitionDown
( pT, p0,
/**/ /**/
p1,
pB, p2 );
View1x2( AB, ABL, ABR );
const int pivotOffset = A01.Height();
A12_STAR_VR.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
p1_STAR_STAR.ResizeTo( p1.Height(), 1 );
//--------------------------------------------------------------------//
A21_MC_STAR = A21;
A11_STAR_STAR = A11;
lu::Panel( A11_STAR_STAR, A21_MC_STAR, p1_STAR_STAR, pivotOffset );
ComposePivots( p1_STAR_STAR, pivotOffset, image, preimage );
ApplyRowPivots( AB, image, preimage );
// Perhaps we should give up perfectly distributing this operation since
// it's total contribution is only O(n^2)
A12_STAR_VR = A12;
LocalTrsm
( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );
A11 = A11_STAR_STAR;
A12 = A12_STAR_MR;
A21 = A21_MC_STAR;
p1 = p1_STAR_STAR;
//--------------------------------------------------------------------//
A12_STAR_VR.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlidePartitionDown
( pT, p0,
p1,
/**/ /**/
pB, p2 );
}
}
inline void
CholeskyUVar3( DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::CholeskyUVar3");
if( A.Height() != A.Width() )
throw std::logic_error
("Can only compute Cholesky factor of square matrices");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary matrix distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ABR.Height() > 0 )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalCholesky( UPPER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MC = A12_STAR_VR;
A12_STAR_MR = A12_STAR_VR;
LocalTrrk
( UPPER, ADJOINT, F(-1), A12_STAR_MC, A12_STAR_MR, F(1), A22 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
LU( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("LU");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() && ATL.Width() < A.Width() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A12_STAR_VR.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A21_MC_STAR.AlignWith( A22 );
A11_STAR_STAR.ResizeTo( A11.Height(), A11.Width() );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalLU( A11_STAR_STAR );
A11 = A11_STAR_STAR;
A21_MC_STAR = A21;
LocalTrsm
( RIGHT, UPPER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A21_MC_STAR );
A21 = A21_MC_STAR;
// Perhaps we should give up perfectly distributing this operation since
// it's total contribution is only O(n^2)
A12_STAR_VR = A12;
LocalTrsm
( LEFT, LOWER, NORMAL, UNIT, F(1), A11_STAR_STAR, A12_STAR_VR );
A12_STAR_MR = A12_STAR_VR;
LocalGemm( NORMAL, NORMAL, F(-1), A21_MC_STAR, A12_STAR_MR, F(1), A22 );
A12 = A12_STAR_MR;
//--------------------------------------------------------------------//
A12_STAR_VR.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A21_MC_STAR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
HPDInverseLVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
PushCallStack("internal::HPDInverseLVar2");
if( A.Height() != A.Width() )
throw std::logic_error("Nonsquare matrices cannot be triangular");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,STAR,MC > A10_STAR_MC(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,MC > A21Trans_STAR_MC(g);
DistMatrix<F,VR, STAR> A21_VR_STAR(g);
DistMatrix<F,STAR,MR > A21Adj_STAR_MR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A10_STAR_VR.AlignWith( A00 );
A21_VC_STAR.AlignWith( A20 );
A10_STAR_MC.AlignWith( A00 );
A10_STAR_MR.AlignWith( A00 );
A21Trans_STAR_MC.AlignWith( A20 );
A21_VR_STAR.AlignWith( A22 );
A21Adj_STAR_MR.AlignWith( A22 );
//--------------------------------------------------------------------//
A11_STAR_STAR = A11;
LocalCholesky( LOWER, A11_STAR_STAR );
A10_STAR_VR = A10;
LocalTrsm
( LEFT, LOWER, NORMAL, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );
A10_STAR_MC = A10_STAR_VR;
A10_STAR_MR = A10_STAR_VR;
LocalTrrk
( LOWER, ADJOINT,
F(1), A10_STAR_MC, A10_STAR_MR, F(1), A00 );
A21Trans_STAR_MC.TransposeFrom( A21_VC_STAR );
LocalGemm
( TRANSPOSE, NORMAL, F(-1), A21Trans_STAR_MC, A10_STAR_MR, F(1), A20 );
A21_VR_STAR = A21_VC_STAR;
A21Adj_STAR_MR.AdjointFrom( A21_VR_STAR );
LocalTrrk
( LOWER, TRANSPOSE,
F(-1), A21Trans_STAR_MC, A21Adj_STAR_MR, F(1), A22 );
LocalTrsm
( LEFT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A10_STAR_VR );
LocalTrsm
( RIGHT, LOWER, NORMAL, NON_UNIT, F(-1), A11_STAR_STAR, A21_VC_STAR );
LocalTriangularInverse( LOWER, NON_UNIT, A11_STAR_STAR );
LocalTrtrmm( ADJOINT, LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
A10 = A10_STAR_VR;
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
A10_STAR_VR.FreeAlignments();
A21_VC_STAR.FreeAlignments();
A10_STAR_MC.FreeAlignments();
A10_STAR_MR.FreeAlignments();
A21Trans_STAR_MC.FreeAlignments();
A21_VR_STAR.FreeAlignments();
A21Adj_STAR_MR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
inline void
TwoSidedTrmmLVar4
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& L )
{
#ifndef RELEASE
CallStackEntry entry("internal::TwoSidedTrmmLVar4");
if( A.Height() != A.Width() )
LogicError("A must be square");
if( L.Height() != L.Width() )
LogicError("Triangular matrices must be square");
if( A.Height() != L.Height() )
LogicError("A and L must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
LTL(g), LTR(g), L00(g), L01(g), L02(g),
LBL(g), LBR(g), L10(g), L11(g), L12(g),
L20(g), L21(g), L22(g);
// Temporary distributions
DistMatrix<F,STAR,VR > A10_STAR_VR(g);
DistMatrix<F,STAR,MR > A10_STAR_MR(g);
DistMatrix<F,STAR,MC > A10_STAR_MC(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> A21_MC_STAR(g);
DistMatrix<F,STAR,VR > L10_STAR_VR(g);
DistMatrix<F,MR, STAR> L10Adj_MR_STAR(g);
DistMatrix<F,STAR,MC > L10_STAR_MC(g);
DistMatrix<F,STAR,STAR> L11_STAR_STAR(g);
DistMatrix<F,STAR,VR > Y10_STAR_VR(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( L, LTL, LTR,
LBL, LBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( LTL, /**/ LTR, L00, /**/ L01, L02,
/*************/ /******************/
/**/ L10, /**/ L11, L12,
LBL, /**/ LBR, L20, /**/ L21, L22 );
A10_STAR_VR.AlignWith( A00 );
A10_STAR_MR.AlignWith( A00 );
A10_STAR_MC.AlignWith( A00 );
A21_MC_STAR.AlignWith( A20 );
L10_STAR_VR.AlignWith( A00 );
L10Adj_MR_STAR.AlignWith( A00 );
L10_STAR_MC.AlignWith( A00 );
Y10_STAR_VR.AlignWith( A10 );
//--------------------------------------------------------------------//
// Y10 := A11 L10
A11_STAR_STAR = A11;
L10Adj_MR_STAR.AdjointFrom( L10 );
L10_STAR_VR.AdjointFrom( L10Adj_MR_STAR );
Zeros( Y10_STAR_VR, A10.Height(), A10.Width() );
Hemm
( LEFT, LOWER,
F(1), A11_STAR_STAR.LockedMatrix(), L10_STAR_VR.LockedMatrix(),
F(0), Y10_STAR_VR.Matrix() );
// A10 := A10 + 1/2 Y10
A10_STAR_VR = A10;
Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );
// A00 := A00 + (A10' L10 + L10' A10)
A10_STAR_MR = A10_STAR_VR;
A10_STAR_MC = A10_STAR_VR;
L10_STAR_MC = L10_STAR_VR;
LocalTrr2k
( LOWER, ADJOINT, ADJOINT, ADJOINT,
F(1), A10_STAR_MC, L10Adj_MR_STAR,
L10_STAR_MC, A10_STAR_MR,
F(1), A00 );
// A10 := A10 + 1/2 Y10
Axpy( F(1)/F(2), Y10_STAR_VR, A10_STAR_VR );
// A10 := L11' A10
L11_STAR_STAR = L11;
LocalTrmm
( LEFT, LOWER, ADJOINT, diag, F(1), L11_STAR_STAR, A10_STAR_VR );
A10 = A10_STAR_VR;
// A20 := A20 + A21 L10
A21_MC_STAR = A21;
LocalGemm
( NORMAL, ADJOINT, F(1), A21_MC_STAR, L10Adj_MR_STAR, F(1), A20 );
// A11 := L11' A11 L11
LocalTwoSidedTrmm( LOWER, diag, A11_STAR_STAR, L11_STAR_STAR );
A11 = A11_STAR_STAR;
// A21 := A21 L11
A21_VC_STAR = A21_MC_STAR;
LocalTrmm
( RIGHT, LOWER, NORMAL, diag, F(1), L11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( LTL, /**/ LTR, L00, L01, /**/ L02,
/**/ L10, L11, /**/ L12,
/*************/ /******************/
LBL, /**/ LBR, L20, L21, /**/ L22 );
}
}
inline void
LVar2( DistMatrix<F>& A )
{
#ifndef RELEASE
CallStackEntry entry("cholesky::LVar2");
if( A.Height() != A.Width() )
LogicError("Can only compute Cholesky factor of square matrices");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
// Temporary distributions
DistMatrix<F,MR, STAR> A10Adj_MR_STAR(g);
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,VC, STAR> A21_VC_STAR(g);
DistMatrix<F,MC, STAR> X11_MC_STAR(g);
DistMatrix<F,MC, STAR> X21_MC_STAR(g);
// Start the algorithm
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
A10Adj_MR_STAR.AlignWith( A10 );
X11_MC_STAR.AlignWith( A10 );
X21_MC_STAR.AlignWith( A20 );
//--------------------------------------------------------------------//
A10Adj_MR_STAR.AdjointFrom( A10 );
LocalGemm( NORMAL, NORMAL, F(1), A10, A10Adj_MR_STAR, X11_MC_STAR );
A11.SumScatterUpdate( F(-1), X11_MC_STAR );
A11_STAR_STAR = A11;
LocalCholesky( LOWER, A11_STAR_STAR );
A11 = A11_STAR_STAR;
LocalGemm( NORMAL, NORMAL, F(1), A20, A10Adj_MR_STAR, X21_MC_STAR );
A21.SumScatterUpdate( F(-1), X21_MC_STAR );
A21_VC_STAR = A21;
LocalTrsm
( RIGHT, LOWER, ADJOINT, NON_UNIT, F(1), A11_STAR_STAR, A21_VC_STAR );
A21 = A21_VC_STAR;
//--------------------------------------------------------------------//
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
}
}
inline void
TwoSidedTrsmUVar5
( UnitOrNonUnit diag, DistMatrix<F>& A, const DistMatrix<F>& U )
{
#ifndef RELEASE
PushCallStack("internal::TwoSidedTrsmUVar5");
if( A.Height() != A.Width() )
throw std::logic_error("A must be square");
if( U.Height() != U.Width() )
throw std::logic_error("Triangular matrices must be square");
if( A.Height() != U.Height() )
throw std::logic_error("A and U must be the same size");
#endif
const Grid& g = A.Grid();
// Matrix views
DistMatrix<F>
ATL(g), ATR(g), A00(g), A01(g), A02(g),
ABL(g), ABR(g), A10(g), A11(g), A12(g),
A20(g), A21(g), A22(g);
DistMatrix<F>
UTL(g), UTR(g), U00(g), U01(g), U02(g),
UBL(g), UBR(g), U10(g), U11(g), U12(g),
U20(g), U21(g), U22(g);
// Temporary distributions
DistMatrix<F,STAR,STAR> A11_STAR_STAR(g);
DistMatrix<F,STAR,MC > A12_STAR_MC(g);
DistMatrix<F,STAR,MR > A12_STAR_MR(g);
DistMatrix<F,STAR,VC > A12_STAR_VC(g);
DistMatrix<F,STAR,VR > A12_STAR_VR(g);
DistMatrix<F,STAR,STAR> U11_STAR_STAR(g);
DistMatrix<F,STAR,MC > U12_STAR_MC(g);
DistMatrix<F,STAR,MR > U12_STAR_MR(g);
DistMatrix<F,STAR,VC > U12_STAR_VC(g);
DistMatrix<F,STAR,VR > U12_STAR_VR(g);
DistMatrix<F,STAR,VR > Y12_STAR_VR(g);
DistMatrix<F> Y12(g);
PartitionDownDiagonal
( A, ATL, ATR,
ABL, ABR, 0 );
LockedPartitionDownDiagonal
( U, UTL, UTR,
UBL, UBR, 0 );
while( ATL.Height() < A.Height() )
{
RepartitionDownDiagonal
( ATL, /**/ ATR, A00, /**/ A01, A02,
/*************/ /******************/
/**/ A10, /**/ A11, A12,
ABL, /**/ ABR, A20, /**/ A21, A22 );
LockedRepartitionDownDiagonal
( UTL, /**/ UTR, U00, /**/ U01, U02,
/*************/ /******************/
/**/ U10, /**/ U11, U12,
UBL, /**/ UBR, U20, /**/ U21, U22 );
A12_STAR_MC.AlignWith( A22 );
A12_STAR_MR.AlignWith( A22 );
A12_STAR_VC.AlignWith( A22 );
A12_STAR_VR.AlignWith( A22 );
U12_STAR_MC.AlignWith( A22 );
U12_STAR_MR.AlignWith( A22 );
U12_STAR_VC.AlignWith( A22 );
U12_STAR_VR.AlignWith( A22 );
Y12.AlignWith( A12 );
Y12_STAR_VR.AlignWith( A12 );
//--------------------------------------------------------------------//
// A11 := inv(U11)' A11 inv(U11)
U11_STAR_STAR = U11;
A11_STAR_STAR = A11;
LocalTwoSidedTrsm( UPPER, diag, A11_STAR_STAR, U11_STAR_STAR );
A11 = A11_STAR_STAR;
// Y12 := A11 U12
U12_STAR_VR = U12;
Y12_STAR_VR.ResizeTo( A12.Height(), A12.Width() );
Hemm
( LEFT, UPPER,
F(1), A11_STAR_STAR.LocalMatrix(), U12_STAR_VR.LocalMatrix(),
F(0), Y12_STAR_VR.LocalMatrix() );
Y12 = Y12_STAR_VR;
// A12 := inv(U11)' A12
A12_STAR_VR = A12;
LocalTrsm
( LEFT, UPPER, ADJOINT, diag, F(1), U11_STAR_STAR, A12_STAR_VR );
A12 = A12_STAR_VR;
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12, A12 );
// A22 := A22 - (A12' U12 + U12' A12)
A12_STAR_VR = A12;
A12_STAR_VC = A12_STAR_VR;
U12_STAR_VC = U12_STAR_VR;
A12_STAR_MC = A12_STAR_VC;
U12_STAR_MC = U12_STAR_VC;
A12_STAR_MR = A12_STAR_VR;
U12_STAR_MR = U12_STAR_VR;
LocalTrr2k
( UPPER, ADJOINT, ADJOINT,
F(-1), U12_STAR_MC, A12_STAR_MR,
A12_STAR_MC, U12_STAR_MR,
F(1), A22 );
// A12 := A12 - 1/2 Y12
Axpy( F(-1)/F(2), Y12, A12 );
// A12 := A12 inv(U22)
//
// This is the bottleneck because A12 only has blocksize rows
Trsm( RIGHT, UPPER, NORMAL, diag, F(1), U22, A12 );
//--------------------------------------------------------------------//
A12_STAR_MC.FreeAlignments();
A12_STAR_MR.FreeAlignments();
A12_STAR_VC.FreeAlignments();
A12_STAR_VR.FreeAlignments();
U12_STAR_MC.FreeAlignments();
U12_STAR_MR.FreeAlignments();
U12_STAR_VC.FreeAlignments();
U12_STAR_VR.FreeAlignments();
Y12.FreeAlignments();
Y12_STAR_VR.FreeAlignments();
SlidePartitionDownDiagonal
( ATL, /**/ ATR, A00, A01, /**/ A02,
/**/ A10, A11, /**/ A12,
/*************/ /******************/
ABL, /**/ ABR, A20, A21, /**/ A22 );
SlideLockedPartitionDownDiagonal
( UTL, /**/ UTR, U00, U01, /**/ U02,
/**/ U10, U11, /**/ U12,
/*************/ /******************/
UBL, /**/ UBR, U20, U21, /**/ U22 );
}
#ifndef RELEASE
PopCallStack();
#endif
}
